If $ a+b+c=4 ; a^2=b^2+c=6 ; a^3+b^3+c^3=8 $ Then find the value of $a^4+b^4+c^4$

Question

If

1. $a+b+c=4$

2. $ a^2=b^2+c=6$ (this is not symmetric equation)

3. $a^3+b^3+c^3=8$

Then find the value of $a^4+b^4+c^4$